STATISTICS I

Question 1

CLASS MIDPOINT

Answer 1

Class 35-39
Using limit. Lower class limit + upper out of 2.
Same for boundaries
34.5+39.5

Question 2

Steps to Draw a Pie Chart:

Answer 2

Angle of a circle =360 degree

1.	Find the Total of the Category Values: Add up all the values to get the total 
2.	Calculate the Angle for Each value Use the formula: Angle of value= value/total value x 360

When done,add all new values and check if they sum up to 360!

Question 3

Finding Percentages and Fractions

How do you find percentage or fraction of a value?

Answer 3

• Percentage = (Value ÷ Total) × 100
• Fraction = Value ÷ Total

Question 4

What formulas do you use for pie charts if given:
Angles?(are shown on the pie chart.)

Answer 4

🔹 If Given Angles
• Value of 1° = Known Quantity ÷ Angle
(If angle isn’t tied to anything, divide by 360)
• Unknown Value = Angle × Value of 1°
• Total Quantity = 360 × Value of 1°
• Fraction = Angle ÷ 360
• Missing Angle = 360° − (Sum of known angles

Question 5

What formulas do you use for pie charts if given: Percentages(are shown on the pie chart.)

Answer 5

If Given Percentage
• Value = (Percentage ÷ 100) × Total

Question 6

What formulas do you use for pie charts if given:Raw numbers (are shown on the pie chart.)

Answer 6

1. Add all values to get Total
   
   2. Use:
      • Angle = (Value ÷ Total) × 360
      • Percentage = (Value ÷ Total) × 100

Question 7

Finding:
•Amount of Money / Value
Missing angle
Fraction of an angle

Answer 7

1. Angle/360 x total amount/value
2. 360-(sum of known angles)
3. Angle/360

Question 8

Should you leave spaces in drawing bar chart?
Where is the x axis and yaxis(frequency axis)

Answer 8

No
Xaxis is the horizontal line. Yaxis is the vertical line.

Question 9

Probability formula

Answer 9

Number of favorable outcome/Total number of outcome

Question 10

How do you label the x-axis when using class boundaries in a histogram?

Answer 10

Label all the boundary values in order:
• e.g. 9.5, 14.5, 19.5, 24.5
Each bar stretches from one boundary to the next, and bars must touch (no gaps).

🧱 Bar 1: 9.5–14.5
🧱 Bar 2: 14.5–19.5
🧱 Bar 3: 19.5–24.5

Question 11

What is mean,median and mode

Answer 11

Mean =average
Median= middle
Model=frequent

Question 12

Formula for mean

Answer 12

Sum of values/number of values
Formula Ex/n

Question 13

Formula for normal or direct numbers

Answer 13

Same as mean. Sum of all values/number of values.
Ex/n

Question 14

Formula for mean with unknown number (one missing number)

Answer 14

Multiply mean x total counts
Add the known values and substract from the total of mean x total count to get the missing number

Question 15

Combining two groups

Answer 15

Sum of group 1 + sum of group 2/ adding of average scores

Sum of groups = mean x total count

Question 16

Correct a wrong value or Finding correct average

Answer 16

1. Calculate the original total:
   Total = Average × Number of values
2. Adjust the total for the wrong value:
   Correct Total = Total − Wrong value + Correct value
3. Find the corrected average:
   Corrected Average = Correct Total ÷ Number of values

Question 17

MEAN FROM A FREQUENCY DISTRIBUTION TABLE (Direct Method)

When to Use This

Formula

Answer 17

Use this when data is given in a frequency table — like scores or ages and how many times each appears.

x=Efx/ef

Where:
• f = frequency (how many times a value occurs)
• x = the value itself (for ungrouped) OR midpoint/class mark (for grouped)
• fx = multiply each value by its frequency
• efx = total of all fx
• ef = total frequency

Question 18

Assumed Mean Method
When to use

Answer 18

When the numbers in the frequency table are large or spread out, class intervals,the Assumed Mean Method makes calculations easier.
x=A+efd/ef

Where:
• A = Assumed Mean (choose any class midpoint close to the center)
• x = class midpoint/the value if there’s no class intervals
• d = x - A = deviation
• f = frequency
• fd = frequency × deviation
• efd = total of all fd
• ef = total frequency

Question 19

When there’s no assumed number given and it’s just large numbers but not intervals how do you get the assume

Answer 19

You get the assume from the values(x)(mark,scores,age….
The middle number

Question 20

Steps to find median

Answer 20

1. Arrange numbers from smallest to biggest.
   
   2. Count how many numbers (let’s call it n).
   3. Check:
      • If n is odd:
      Median position = (n + 1) ÷ 2
      → The number at that position is the median.
      • If n is even:
      Median = (middle 1 + middle 2) ÷ 2

Question 21

From Grouped Frequency Table (Class Intervals)

Answer 21

Use full median formula:
L+(n/2-cf all out of f) x class width
• L = lower boundary of median class
• N = total frequency
• CF = cumulative frequency before median class
• f = frequency of median class
• c = class width

Question 22

Median From Ungrouped Frequency Table

Answer 22

Use cumulative frequency to locate middle item
• Follow:
1. Find ef = N
2. Calculate N/2
3. Find class where that item lies
4. Read off the value (not the frequency)